According to the credits, some bloke called Chris O'Neil, who may be the same one who played George Harrison in Backbeat (although his voice sounds more like Paul McCartney to me).
however if you look up temper trap & their song sweet disposition you will find this is the song
Chat with our AI personalities
Bowling for soup
Chris Madin
The Who - Won't Get Fooled Again
One of them is 'Ever So Shy' by General Fiasco.
The original version of the Top Gear music is 'Jessica' by the Allman Brothers Band.